It seems those things which we assert or claim to know are either 1) groundless assumption, or 2) things which rest on some other pieces of knowledge or assertion. Now, for the latter category, it we trace the supporting knowledge or principles through sufficient steps, we always arrive at a groundless assumption.
For example, we ‘know’ that “There sun is larger than the moon”, because we have read it in books. We ‘know’ that those books can be believed because we trust the expertise of the authors. We trust the expertise of the authors because the majority of other people seem to do so. But why should we give any particular credence to a majority opinion? Here we have a groundless assumption. The fact that many people agree on this groundless assumption is no proof of its truth, since we know that, in the past, the majority have often agreed upon errors.
And, if the knowledge is derived from our perceptions, why should we trust them? It is only our perceptions which verify our perceptions, and thus the whole complex is circular. To trust our perceptions seems to be a groundless assumption.
Now, if all our knowledge, if traced back far enough, is ultimately based on some groundless assumption, why not simply boldly embrace any groundless assumption at the beginning? Surely a piece of ‘knowledge’ which rests, ultimately, on some fundamental groundless assumption has no more merits than the groundless assumption itself, and surely all groundless assumptions are of equal truth value.
Hence it would seem that what passes as ‘knowledge’ is no better than pure unsupported assertions, since one is no more secure in its epistemological basis than the other.
It would seem you are defining groundlessness as unproven and then what is unproven as an assumption.
However what is evident to the senses or to, as Aristotle would call it, “intuitive reason” is not proven but also not an assumption. It is evident. That is, acquaintance with life shows that sense experience (including implicit judgments not just raw impressions on sense organs) in the vast majority cases is trustworthy or self-correcting. And reflection shows that first principles, evident (or self-evident) to the intellect, are involved in all knowing and thinking.
To your point sense perception is shaped by the given historical, cultural, linguistic tradition in which one find oneself. But that too is also corrected and adjusted by further experience with reality.
I actually find this question very interesting and have accumulated a number of texts on the subject.
Some quotes from just one work:
A postulate is not self-evident; what is self-evident is not postulated, it is seen.”
[Etienne Gilson, *Thomist Realism And The Critique of Knowledge (San Francisco: Ignatius Press, 1986), p. 51, n. 32]
“What, then, is a postulate? It is a proposition that must be accepted as true, although it is neither evident nor demonstrable. Any manual on the logic of the sciences will present this definition. If the proposition in question is evident, it is an axiom or a principle, not a postulate. If the proposition is demonstrable, it is neither a postulate nor a principle, but a conclusion.”
[Etienne Gilson, *Thomist Realism And The Critique of Knowledge (San Francisco: Ignatius Press, 1986), p. 179.]
“No one really doubts that sight, touch, hearing, taste and even smell are normally competent to attest to existence, and whenever it is necessary it verify the existence of anything it is to the testimony of one or more of the senses that we turn. This conviction of the reliability of our senses is simply the self-evidence of our experience. Since we are here concerned with self-evidence, it is futile to demand a demonstration. All we can do for someone who does not see something is to point it out to him. If he then sees it, well and good, but we cannot prove to him that he does see it.”
[Etienne Gilson, *Thomist Realism And The Critique of Knowledge (San Francisco: Ignatius Press, 1986), p. 181]